The relative permeability and electrical conductivity of the pan material, both of which vary with temperature, play an important role in thermal power of induction cooker system. A series of finite element models, including a variable relative permeability electromagnetic model, a variable electrical conductivity electromagnetic model, and an electromagnetic and thermal coupling model, have been built by ANSYS software to analyze the variation of the thermal power with relative permeability and electrical conductivity in this paper. It is indicated that thermal power increases with the relative permeability increasing, but its growth rate decreases. When the electrical conductivity increases, thermal power increases, reaches a peak value, and then decreases. Considering the variation of the relative permeability and electrical conductivity with pan temperature, the simulation results show that thermal power decreases a lot when the temperature of the material exceeds a definite value due to the low relative permeability in this case. Finally, the induction heating mechanism is clearly understood and the simulation results provide useful guidance for induction cooker design.